Repulsive van der Waals forces due to hydrogen exposure on bilayer graphene

We consider the effect of atomic hydrogen exposure to a system of two undoped sheets of graphene grown near a silica surface (the first adsorbed to the surface and the second freestanding near the surface). In the absence of atomic hydrogen, the van der Waals force between the sheets is attractive at all separations, causing the sheets to come closer together. However, with the addition of atomic hydrogen between the sheets, the long-range van der Waals interaction turns repulsive at a critical concentration. The underlying triple layer structure (SiO${}_2$–atomic hydrogen gas–air) gives rise to a long-range repulsion that at large-enough separations dominates over the more rapidly decaying attraction between the two-dimensional undoped graphene sheets (and between the outer graphene sheet and SiO${}_2$). This may be an avenue to tune the separation between two graphene sheets with the gas concentration. The doping of the graphene layers increases the attractive part of the interaction and hence reduces the net repulsive interaction.

Figure 1

Geometry considered in this work: Two graphene sheets, undoped or doped, a distance $L$ apart, one adsorbed to a SiO${}_2$ substrate and the other freestanding; the space between them is filled with a gas.

Figure 2

The dielectric function at imaginary frequencies for SiO${}_2$ (upper curve) and atomic hydrogen gas at a concentration of $n_{\mathrm{H}}$ = 4 × 10${}^{22}$ cm${}^{-3}$ (lower curve).

Figure 3

The van der Waals interaction energy between two undoped graphene sheets (one adsorbed to SiO${}_2$, one freestanding a distance $L$ from the surface) considering two different concentrations ($n_{\mathrm{H}}$) of hydrogen atoms between the sheets.

Figure 4

The van der Waals interaction energy between two undoped graphene sheets (one adsorbed to SiO${}_2$, one freestanding a distance $L$ from the surface) considering a specific concentration of hydrogen atoms, hydrogen molecules, and helium atoms between the sheets.

Figure 5

The van der Waals interaction energy between two graphene sheets (one adsorbed to SiO${}_2$, one freestanding a distance $L$ from the surface) for a specific concentration of atomic hydrogen between the sheets. The upper curve is for undoped graphene while the lower curves are for different doping concentration. We see that the doping reduces the repulsive van der Waals interaction.

Figure 6

The total van der Waals interaction energy between two undoped graphene sheets (one adsorbed to SiO${}_2$, one freestanding a distance $L$ from the surface) as a function of concentration of hydrogen atoms between the sheets.

Figure 7

Van der Waals energy between two freestanding graphene sheets. The solid curve is the result from the standard approach only including contributions from the valence bands (π bonds) [15]. The dashed curve is an estimated contribution from the σ bonds.